Tropes

First published Mon Sep 9, 2013

According to trope theory, the world consists (wholly or partly) of
ontologically unstructured (simple) abstract particulars or, as they
are normally called, tropes. Tropes are abstract yet
they are not universal, they are particular yet they
are not concrete. In accepting the existence of entities
characterized in this (unusual) way, the theory can be said to occupy
a middle position in between classical nominalism—according to
which all there is are concrete particulars—and
classical realism—according to which there is a separate and
fundamental category of abstract universals. And this, it has
been argued, means that trope theory avoids well-known problems with
both of those views. By accepting the existence of abstract entities
(like shapes and weights), the trope theorist is able to explain how
distinct concrete particulars can be simultaneously similar to, and
different from, each other. And this is something the classical
nominalist, whose basic ontology is more coarse-grained, has been
accused of not being able to do (for a famous instance of this
critique of classical nominalism, see Armstrong 1978). And by not
accepting the existence of universals, she avoids having to accept the
existence of a kind of entity many find mysterious, counterintuitive,
and “unscientific” (Schaffer 2001: 249f.; Molnar 2003:
22–25; and Armstrong 2005: 310). Apart from this very thin core
assumption—that there are tropes—different trope
theories need not have very much in common. Most trope theorists (but
not all) believe that there is nothing but tropes. Most trope
theorists (but, again, not all) hold that resemblance between concrete
particulars is to be explained in terms of resemblance between their
respective tropes. And most (but not all) hold that resemblance
between tropes is determined by their primitive intrinsic nature. In
fact, even to call one's posits “tropes” is by some
considered problematic (see especially Bacon
2011).[1] In this
entry, different views on the nature and individuation of tropes, on
how tropes relate to both universals and concrete particulars, and on
how tropes might or might not be used to (dis)solve well known
problems in philosophy, are introduced.

The father of the contemporary debate on tropes was D. C. Williams
(1997 [1953]; 1963; 1986). In 1953, he published “On the
Elements of Being I” in which he argued for a
one-category theory of tropes (for the first time so labeled), a
bundle theory of concrete particulars, and a resemblance class theory
of universals. All of these have become elements of what is now
considered the “standard” view of tropes (a view that will
be further spelled out and explained in sections 2–4). But
Williams was in all probability not the first to posit the existence
of trope-like entities. Who to count among his trope-theoretical
predecessors is unavoidably contentious. It will depend on how the
nature of the trope is conceptualized, and on what the essential
elements of a trope—or trope-like—theory are
taken to be, matters on which opinions have been very much
divided. Here the history of trope theory can only be cursorily
treated (for a more thorough account, see Mertz 1996 and Mulligan et
al. 1984).

Even if there are those who think that both Plato and Aristotle
posited entities somewhat like what later thinkers would refer to as
“tropes” (see Mertz 1996: 83–118), and even if (most
likely even stronger) reasons exist for holding that many of the
medieval thinkers (including Aquinas, Duns Scotus, and Suarez) also
accepted the existence of trope-like entities, it is in the writings
of 19th century German-speaking philosophers that the
earliest and most systematic pre-Williams “trope”-theories
can be found (as argued by e.g., Mulligan et al. (1984: 293)). The
clearest example of an early trope theorist of this variety is
undoubtedly Edmund Husserl. In the third part of his Logical
Investigations (2001 [1900/1913]), Husserl sets out his theory of
“moments,” which is his name for the world's abstract (and
essentially dependent) individual parts, in order to then clearly
distinguish and relate them to the world's concrete parts using his
theory of “foundations,” a species of the kind ontological
dependence (for more on Husserl's version of the trope theory, see
Correia 2004 and Beyer
2011).[2]

Husserl developed his version of the theory in a purely
phenomenological framework. That is, he posited tropes as (one of) the
fundamental constituents of phenomenal reality. This was also
the setting for the trope-like entities posited by G. F. Stout (1921;
1952),[3] Roman
Ingarden (1964 [1947–1948]), and Ivar Segelberg (1999
[1945, 1947,
1953]),[4]
among others. Williams's own views are not
so easily classified. Although he maintained that all our knowledge
rests on perceptual experience, he agreed that it should not be
limited to the perceptually given and that it could be extended beyond
that by legitimate inference (see Campbell et al. 2013). That more or
less all the post-Williams proponents of tropes treat their
posits as the fundamental constituents of mind-independent,
not phenomenal, reality, is however clear. In fact, several of the
theory's proponents have emphasized not just that there is a
distinction, but also that there may be a (radical) difference between
reality as it appears to us, and reality as it is independently of how
it appears, and they have then spent much time and effort trying to
overcome the epistemological challenges their views would seem to
entail (see e.g., Heil 2003).

After Williams, the second most influential trope theorist is arguably
Keith Campbell (1997 [1981]; 1990). Campbell more or less adopted the
basics of Williams's (standard) theory and then further developed and
defended it. Later proponents of variants of the standard view include
John Bacon (1995), Anna-Sofia Maurin (2002), and Douglas Ehring (2011)
(although Ehring treats sameness of tropes in class-primitivist terms
rather than in terms of resemblance classes (see
section 3.1)). A very influential paper also arguing for a version
of the standard view (although inspired more by Husserl than by
Williams) is “Truth-Makers” (Mulligan et al. 1984). This
paper defends the view that tropes are essentially dependent entities,
the objects of perception, and the world's basic truthmakers.
Proponents of trope theories which posit tropes as one of
several fundamental categories include John Heil (2003) and
George Molnar (2003), who both defend ontologies that include (but are
not limited to) tropes understood as powers, and E. J. Lowe (2006), who
counts tropes as one of four fundamental categories. Even more
“unorthodox” are the views set forth by Arda Denkel (1996),
who argues that tropes constitute a derived category because they must
be bundled, and, not least, D. W. Mertz (1996), whose trope-like
entities are categorized as a kind of
relations.[5]
We will return to the views expressed by all of
these philosophers (and then some) in what follows.

In philosophy, new posits are regularly introduced by being compared
with, or likened to, an already familiar item. Tropes are no exception
to this rule. In fact, tropes have been introduced by being compared
with and likened to not one but two distinct but equally
familiar kinds of things: the property and the substance. Consider the
way Williams first introduces his fundamental posits (1997 [1953]:
113). Williams famously asks the reader to imagine a situation in
which there are three distinct but similar lollipops. Each lollipop,
more precisely, is
partially similar to (and partially different from) each other
lollipop. To say of any two things a and b that they
are “partially similar,” we are told, is to say that a part
of a is wholly similar to a part of b. And in this
particular case, Williams tells us, the lollipops are partially similar
at least because their sticks and shapes, unlike
their colors and tastes, are wholly similar.

But what kinds of things are the shapes, colors and tastes of the
lollipops, and how do they compare with such things as the lollipops
themselves, their sticks, and their heads? Given the way things have
been set up, these questions can now be given two seemingly very
different answers. The individual shapes, colors and tastes of the
lollipops, first, are the sorts of things that characterize
lollipops, they are ways the lollipops are, they are
properties the lollipops have. Under this view, the shapes,
colors and tastes of lollipops are unlike their sticks and
heads which do not likewise characterize lollipops, and they are unlike
the lollipops themselves which do not characterize either their sticks
and heads or anything else for that matter. Alternatively, the
individual shapes, colors and tastes of the lollipops are the sorts of
things of which lollipops are made up, they are the parts—the
substances—of which the lollipops, their sticks, and their
heads consist. Under this view, the shapes, colors and tastes of the
lollipops are like the sticks and heads of lollipops, and they
are like the lollipops themselves (which could, at least in theory, be
parts of, and hence make up, some further thing). Williams himself
seems to lean more towards viewing his posits as kinds of substances.
Names for tropes, he claims, should not be understood as abbreviated
definite descriptions of the kind “the ɸ-ness of
x”. Instead, to name a trope should be likened with
baptizing a child or with introducing a man “present in the
flesh,” i.e., ostensively (Williams 1997 [1953]: 114). But
opinions are clearly divided on this matter. Mulligan et al. (1984),
who seem to regard their tropes more as kinds of properties, argue to
the contrary that the correct (in fact the only) way to refer to tropes
is precisely by way of expressions such as “the ɸ-ness of
x” (or, possibly, “x’s
ɸ-ness”). And this, they claim (again pace
Williams), is because tropes are essentially of some object,
because they are ways the objects are (for another expression of this
view, see Heil 2003: 126f).

Does one's choice of model for the trope make more than a merely
verbal difference to one's theory of tropes? This matter is very
seldom explicitly discussed by the trope proponents (Bacon 1995,
1–2 represents one rare exception). Judging from what the
trope-proponents do more than from what they say,
the consensus seems to be that it does not. Rather, tropes are by
their nature such that they can be adequately
categorized both as a kind of property and as a kind
of substance. That tropes can have this “double nature”
has however been repeatedly questioned by a number of the theory's
critics.

One such critic is Jerrold Levinson. In an early paper he points out
that although objects can be said to have attributes both in the sense
of properties and in the sense of what he calls qualities, having a
property—being red—amounts to being in a certain condition
whereas having a quality—redness—amounts to
“partaking of a certain stuff”. And this, he claims, means
that although qualities can be particularized, properties cannot. He
argues: “[though] [o]ne can have a bit of redness here and a bit
there,” one cannot have “a bit of being red here
and another bit there—being red, a condition, is had by
each object as a unity or not at all” (Levinson 1980: 107).
Therefore, he concludes, tropes cannot be conceived of as a kind of
property. More than twenty-five years later, Levinson returns to the
question of the nature of the trope, but now in an even more
pessimistic mood. As “the supposition of qualities, i.e.,
abstract stuffs as distinct from properties, i.e., conditions, is
ontologically extravagant and conceptually outlandish,” he now
argues, “one cannot seriously propose that there are abstract
stuffs, things just like familiar material stuffs except that they are
abstract” (Levinson 2006: 564). Therefore, tropes cannot be
conceived of either as a kind of property or as a kind of
quality (i.e., as a substance). But then tropes cannot be
conceptualized, period. Therefore, Levinson concludes, there are no
tropes.

The ambiguous way in which tropes are for the most part introduced is
also criticized by Chrudzimski (2002). According to him, to
conceptualize the trope as a property—as a way things
are—means understanding it as an entity with a
propositional structure (see Levinson 1980: 107 for a similar
view). Not so if the trope is understood as a kind of substance. Thus
understood, the trope is an unstructured, ontologically simple,
entity. But this is problematic. For, Chrudzimski argues, although
tropes understood as properties are suitable as semantically efficient
truthmakers (in the sense imagined by Mulligan et al. 1984) the same
is not true of tropes understood as substances. And, conversely,
though tropes understood as substances are suitable candidates for
being that from which both concrete particulars and abstract
universals can be constructed
(see section 3),
tropes understood as properties are not. However we conceive
of them, therefore, tropes are entities unable to play both
of the roles their proponents have taken them to play, and this
considerably diminishes the theory's appeal.

Now, both Levinson's and Chrudzimski's pessimistic conclusions can
arguably be resisted. One reason for such resistance is that it is not
clear why one cannot seriously propose that there can be
“abstract stuffs.” Levinson offers us little more than an
incredulous stare in defense of this conclusion, and incredulous
stares are well-known for lacking the force to convince those not
similarly incredulous. Another reason for resistance is that, in order
for Chrudzimski's argument to go through, a rather substantial
assumption about truthmaking needs to be accepted. We need to accept,
that is, that in general, complex truths require complex
(propositionally structured) truthmakers, and this is, as a
matter of fact, not an assumption that most proponents of truthmaker
theory are willing to accept (see e.g., Mulligan et al. 1984).

As we have just seen, according to some critics of trope theory, to
say of the trope that it is a kind of property is to impute in it a
complex (propositional) structure. What exists when the trope picked
out by the expression “the ɸ-ness of x”
does, on this view, is the complex state of affairs that x is
ɸ. More or less all trope proponents disagree. To
conceptualize tropes as ways things are at most entails that
tropes cannot exist except as one of the constituents of
something complex: the state of affairs that x is ɸ. But
that tropes are one of the constituents of a complex state of affairs
does not make them complex. Tropes are still simple, not further
ontologically analyzable,
entities.[6]

So, tropes are simple. But if they are, Chris Daly (1997 [1994]) has
argued, then there must be some reason for preferring a theory of
simple tropes over a theory of complex states of affairs. More
precisely, in order for trope theory to be justified, there must be
something we can do, some problem we can solve, with the help of
simple tropes that cannot be done or solved with the help of a
substance/substrate exemplifying a universal. But, Daly claims, there
isn't. Every reason we can think of for the existence of (simple)
tropes is likewise a reason for the existence of (complex) states of
affairs. But this means that there is no reason for thinking that
there are tropes. Therefore, trope theory should be abandoned.

Not surprisingly, trope proponents disagree. If every reason to think
that there are tropes is also a reason to think that there are states
of affairs, first, then surely this does not mean that
no reason exists for thinking that there are tropes. What we
lack is at most a reason for preferring tropes over states of
affairs. That we do have reason to prefer a theory of tropes over one
of states of affairs should however be obvious. After all, trope theory
is (or at least, it can be) a one-category theory, a theory of states
of affairs—which posits the existence of substrates
instantiating universals—is not. And one-category
theories ought to be preferred over many-category theories for reasons
of ontological parsimony. Also, states of affairs are partly
constituted by what most proponents of tropes would call
“mysterious” universals, entities able to, among other
things, “fully” exist in more than one place at one moment
in time. Tropes are not. And surely, what is less mysterious ought to
be preferred over what is more mysterious? And so on. More importantly,
trope-proponents have argued, it is far from clear that there are
no explanatory tasks which can only be solved with recourse to
(simple) tropes. In fact, arguments can be presented for why there are
several explanatory tasks of this kind. The most common
suggestions (including the sometimes heated debate they have
occasioned) are set out in sections
3–4.[7]

According to a number of prominent trope critics, even if Daly's
objection can be defused, trope theory is still in serious
trouble (for different versions of this argument, see Armstrong 2005:
310; Brownstein 1973: 47; Hochberg 2001: 178–179 and 2004: 39;
and Moreland 2001: 70). In Herbert Hochberg's words (2004: 39):

Let a basic proposition be one that is either atomic or the negation
of an atomic proposition. Then consider tropes t and t* where “t
is different from t*” and “t is exactly similar to
t*” are both true. Assume you take either
“diversity” or “identity” as primitive. Then
both propositions are basic propositions. But they are logically
independent. Hence, they cannot have the same truth makers. Yet,
for…trope theory /…/ they do and must have the same
truth makers. Thus the theory fails.

If tropes are simple, is the argument, then what makes it true that
this shape-trope is exactly similar to that
shape-trope must be the same thing as that which makes it true that
they are distinct. But this violates what appears to be a truly
fundamental principle, namely that logically independent basic
propositions—in this case that t and t* are exactly
similar and that t and t* are distinct—must have
distinct truthmakers. Therefore, tropes cannot be simple.

This argument fails, a number of trope proponents have suggested,
because what it at most manages to demonstrate, is that the trope
theorist must deny that logically independent basic
propositions have distinct truthmakers, not that this denial is
impossible. Tropes can be simple. All the argument
tells us is that, to hold that they are comes at a certain
(theoretical) price. A price the trope proponent is willing to pay. The
reason the argument fails, moreover, is that it misrepresents the
truthmaker theory it assumes. According to truthmaker theory, the trope
proponent points out, there is no one-one correlation between truths
and that which makes them true (see Mulligan et al. 1984: 296). But
this is the same as to say that, according to truthmaker theory, if two
truths are (logically) distinct, it does not follow that their
truthmakers are likewise (ontologically) distinct. But, of course, that
it does is the assumption which drives the objection. Once this
assumption is removed, therefore, the argument's conclusion no
longer follows from its premises (for one example of this sort of
defense, see Robb (as quoted in Armstrong 2005:
310)).[8]

Tropes may be individuated in at least three ways. First, they may be
individuated with reference to the objects that “have”
them:[9]

Object Individuation (OI):
For all tropes
a and b such that a exactly resembles
b, a = b iff a belongs to the same
object as b does, and a ≠ b iff
a belongs to an object that is distinct from the object to
which b belongs.

A good thing about this way of individuating tropes is that it mirrors
the way we normally refer to them (as e.g., “the
shape of the lollipop” or as “Socrates'
snubnosedness”). A not so good thing about it is that, for
someone who thinks that objects are bundles of tropes (which is the
standard trope-theoretical view of concrete particulars,
see section 3.2), to individuate tropes with
reference to the objects that “have” them is circular (see
Schaffer 2001: 249 and Ehring 2011: 77). Of course, if the concrete
particular is understood instead as a substrate in which a number of
tropes are instantiated (a view proposed by Martin (1980) and by Heil
(2003)) individuation can be non-circularly accounted for using
OI. For in that case, the substrate will carry the individuating
burden. Unfortunately, this leaves the individuation of the substrate
still unaccounted for, and so we appear to have gotten nowhere (see
Mertz 2001). For these reasons no trope theorist has explicitly
endorsed OI.

Spatiotemporal Individuation (SI): For all
tropes a and b such that a exactly
resembles b, a = b iff a is at
zero distance from b, and a ≠ b iff
a is at non-zero distance from b.

Again, this is an account of trope individuation that accords well
with the way tropes are normally picked out. It is also an account on
which two arguably empty possibilities that the trope theorist would
otherwise have to countenance—swapping and
piling—are ruled out (what swapping and piling is,
whether or not SI really does rule them out, and whether or not, if it
does, this is such a good thing, will be discussed in the next
section). In spite of this, the great majority of the trope theorists
(Schaffer (2001) being one important exception) have opted instead for
a primitivist principle of individuation (see Ehring 2011: 76 for
alternative statements of this principle, see also Schaffer 2001: 248 and
Campbell 1990: 69):

Primitivist Individuation (PI): For all tropes
a and b, a = b iff a =
b, and a ≠ b iff a ≠
b.

More or less all arguments proposed in support of PI
have—naturally enough—been arguments for why tropes ought
not to be individuated with reference to their spatiotemporal
position. According to what is probably the most influential such
argument (an argument that changed Campbell's mind in favor of
PI, see Campbell 1990: 55f., see also Moreland 1985: 65), SI should be
rejected because if it is not, the (non-empty) possibility that reality
(or parts of reality) could be non-spatiotemporal is ruled out from
the
outset.[10]
Proponents of SI remain unimpressed. True, if SI is accepted, the
trope theorist must
deny that reality could be non-spatiotemporal. But this, they
argue, is not really a problem as long as the claim that reality is
necessarily spatiotemporal can be independently justified. And it can
be.[11] On the
other hand, if PI (but not SI) is accepted, the trope theorist
must accept the phenomena of “swapping” and
“piling”. That these are empty possibilities can however
be easily demonstrated. Therefore, SI and not PI ought to be adopted
as the most plausible principle of individuation. In the next section,
the debate to which this and related claims (about swapping and
piling, but also about the related phenomena of sliding, pyramiding,
and stacking) has given rise is set out.

According to the so-called “swapping argument” (first
formulated in Armstrong 1989: 131–132, see also Schaffer 2001:
250f; Ehring 2011: 78f.), if properties are tropes, two distinct yet
exactly similar tropes might swap places (this redness here
might have been there, and vice versa). The result,
post-swap, would then be a situation which is ontologically distinct
from that pre-swap. But as the swap makes no detectable difference in
the world, empirically/causally the pre- and post-swap situations
would nevertheless be the same (see LaBossiere 1993: 262, for an
argument to the contrary). But then, if we accept the (arguably
reasonable) Eleatic principle according to which only changes that
matter empirically/causally count as genuine, trope-swapping is ruled
out. Therefore, trope theory should be rejected. This objection can
be put either in terms of object swapping (the two tropes
swap object), or in terms of position swapping (the two
tropes swap position). Armstrong formulates the objection in terms of
object swapping, but, as Ehring has pointed out (2011: 79), the
objection is strengthened if formulated in terms of position. For, to
rule out object swapping, all you need to do is add that tropes are
“non-transferable” in the sense that they must
belong to some specific object. But this does not solve the problem
with position swapping. For, even if tropes are non-transferable, two
exactly similar objects, including the tropes they “have”,
could still swap position with the same presumably
problematic result.

Appearances perhaps to the contrary, to accept SI does not immediately
block either object- or positional trope swapping (Schaffer 2001:
250). For, as stated, SI is a principle about trope individuation that
holds intra-worldly: within any given world, no two exactly
similar tropes are at zero distance from each other. Swapping, on the
other hand, concerns what is possibly true (or not) of exactly similar
tropes considered inter-worldly. As stated, therefore, SI
neither does nor doesn't preclude swapping. That is all very well, as
there is one distinct possibility that it would be unfortunate if our
principle of individuation did block, namely the
possibility—called sliding—that this red-trope
here could have been there had the wind blown
differently (Schaffer 2001: 251). To get the desired result (i.e., to
block swapping while allowing for sliding), Schaffer has therefore
suggested, trope theory ought to be combined, not just with SI, but
also with a Lewisian counterpart theory of transworld identity (see
Lewis 1986). The result would then be an account of trope individuation
according to which exactly resembling tropes are intra-worldly
identical if they inhabit the same position in space-time, and
according to which they are inter-worldly counterparts, if
they are distinct, yet stand in sufficiently similar distance- and
other types of relations to their respective (intra-worldly) neighbors.
With this addition in place, Schaffer claims, sliding is made possible,
because (2001: 253):

On the counterfactual supposition of a shift in wind, what results is
a redness exactly like the actual one, which is in perfectly
isomorphic resemblance relations to its worldmates as the actual one
is to its worldmates, with just a slight difference in distance with
respect to, e.g., the roundness of the moon.

Yet swapping is disallowed. Because,

…the nearest relative of the redness of the rose which is
here at our world would be the redness still here
‘post-swap’. The redness which would be here has exactly
the same inter- and intraworld resemblance relations as the redness
which actually is here, and the same distance relations, and hence is a
better counterpart than the redness which would be there.

Against Schaffer's suggestion it has been argued that, although
combining your views with a Lewisian counterpart theory does solve the
swapping problem, it does not provide you with a reason for preferring
SI over PI. For, PI combined with a Lewisian counterpart
theory also prevents swapping. It is, in other words, the
counterpart theory, and not SI (or PI), which does all the work. More
interestingly, it is not clear that swapping ought to be ruled out
after all. For, according to Ehring, there are circumstances in which
a series of slidings constitute one case of swapping. Therefore, if
sliding is possible (which it certainly seems to be), so is swapping
(Ehring 2011: 81–85).

Now, even if swapping does not give us a reason to prefer SI over PI,
perhaps its close cousin “piling” does. Consider a
particular red rose. Given trope theory, this rose is red because it
is partly constituted by a redness-trope. But what is to
prevent more than one—even indefinitely
many—exactly similar red-tropes from thus partly constituting
this rose? If properties are tropes, the objection goes: nothing. Now,
the existence of indefinitely many exactly similar red-tropes piled on
top of the original one, makes no empirical/causal difference to the
world. Given a (plausible) Eleatic principle, therefore, the
possibility of piling is empty. Therefore, trope theory ought to be
rejected (this argument was first formulated in Armstrong 1978: 86;
see also Simons 1994: 558; and Schaffer 2001: 254, fn. 11).

Now, if tropes are individuated with reference to their spatiotemporal
position—if SI is accepted—the possibility of piling is
immediately blocked. That this should be taken to count in favor of SI
has however been questioned. For, again according to Ehring (2011:
87ff.), as there is a kind of
piling—“pyramiding”—that does
represent a genuine possibility, the possibility of piling in general
ought not to be ruled out. To the contrary, the fact that SI rules out
piling (and thereby pyramiding) is a reason to adopt PI. Against this,
Schaffer has argued that although pyramiding (an example being a 5kg
object consisting of five 1kg tropes) is not as clearly objectionable
as more problematic kinds of piling (called “stacking”) it
ought nevertheless to be rejected. Most importantly, this is because
pyramiding faces a serious problem with predication: if admitted, it
will be true of the 5kg object that “It has the property of
weighing 1kg” (Schaffer 2001: 254). Against this, Ehring has
pointed out that to say truly of the 5kg object that “It has the
property of weighing 1kg” is at most pragmatically odd, and
that, even if this oddness is regarded as unacceptable, to avoid it
would not require the considerable complication of one's theory of
predication imagined by Schaffer (Ehring 2011: 88–91). Neither
swapping nor piling therefore turn out to be the “kiss of
death” they are presented as being by the foes of trope
theory. Nor, it seems, does their possibility (or not) give us strong
reasons to prefer one principle of individuation over another.

As we have seen, tropes can be conceptualized, not just as
particularized ways things are, but also, and on some
versions of the trope theory, primarily, as that out of which
everything else is constructed (see section
2.1). Thus conceived, it has been argued, tropes must be able to
fulfill at least two important constructive tasks: that of making up
(the equivalent of) the realist's universal, and that of making up
(the equivalent of) the nominalist's concrete particular. But the
attempt to fulfill either of these tasks, critics claim, leads to
trouble. Most problematically, it has been repeatedly suggested, both
kinds of construction lead to the generation of an infinite
regress. Whether or not they do, and whether or not, if they do, this
regress is vicious, has been the topic of much debate. In the
following two sections, this debate is summarized.

How can distinct things have one thing in common? This is the problem
of “the One over Many” (see Rodriguez-Pereyra
2000). Universals provide a straightforward solution to this problem:
Distinct things can have one thing in common, because there
is one thing—the universal—which characterizes
each of them individually. The trope theorist—at least the trope
theorist who does not accept the existence of universals in addition
to
tropes[12]—does
not have recourse to entities
that can be likewise identical in distinct instances, and must
therefore come up with a slightly more complicated solution to this
problem. She must “build” something able to do the same
problem-solving work the universal does, using only her abstract
particulars.

The standard solution (i.e., the solution proposed by the majority of
the trope theorists) is to say that distinct objects
“share” a property if (some of) the tropes characterizing
each of them individually exactly resemble each other (see
Williams 1997 [1953]: 117–118; and Campbell 1990:
31f).[13] But
what does this entail, ontologically speaking? What exists when
distinct tropes exactly resemble each other? Two different answers
have been
proposed.[14]
Either, what exists is nothing but the
resembling tropes themselves, or it is those same tropes plus a
(trope-)relation of exact resemblance. Both suggestions have been
rejected by the theory's critics.

The most convincing reason for thinking that nothing but the
resembling tropes is needed to account for trope resemblance is
provided by (one aspect of) the nature of exact resemblance itself.
Exact resemblance is an internal relation; it supervenes on whatever
it relates. Once the resembling tropes exist, therefore,
so must their exact resemblance. But then, given a
“sparse” ontology—an ontology according to which
only what is minimally required to make true all truths
exists—we have no reason to posit exact resemblance in
addition to its relata (for more on what makes something a
“sparse” ontology, see Schaffer 2004). Sparse ontologies
can be independently justified (see Armstrong 1978 for a classic
defense). Therefore, what exists when distinct tropes exactly resemble
each other—and so what plays the role of the realist's
universal—is nothing but the resembling tropes themselves (this
view has been defended in e.g., Campbell 1990: 37f.; and in Williams
1963: 608). In Armstrong's words
(1989:
56)):[15]

…exact resemblance is an ontological free lunch. The
truth-maker, the ontological ground, that in the world which makes it
true that the tie holds, is simply the resembling things. More
precisely … the ontological ground is the particularized nature
of these things. The tie is not something extra.

Alternatively, exact resemblance has been regarded as a
(relation-)trope, and hence as an addition to the tropes it relates.
The main problem with this view is that it appears to gives rise to a
version of Russell's famous resemblance regress (first formulated in
his 1997 [1912]: 48, see also Küng 1967). In Daly's words (1997
[1994]: 149):

Consider three concrete particulars which are the same shade of red
… each of these concrete particulars has a red trope—call
these tropes F, G, and H—and these
concrete particulars exactly resemble each other in colour
because F, G, and H exactly resemble each
other in colour. But it seems that this account is incomplete. It
seems that the account should further claim that resemblance tropes
hold between F, G, and H. That is, it seems
that there are resemblance tropes holding between the members of the
pairs
F and G, G and H, and F
and H … Let us call the resemblance tropes in question
R1, R2, and
R3 … each of these resemblance tropes in
turn exactly resemble each other. Therefore, certain resemblance tropes
hold between these tropes … we are launched on a regress.

This regress is a problem only if it is a vicious regress.
But, it has been suggested, at least two reasons exist for thinking
that it is not. According to Campbell, first, the regress is benign
because “[i]t proceeds in a direction of greater and greater
formality and less and less substance” (1990: 35–36). This
is not a very good reason for thinking that the regress is
unproblematic, however. It is hard to see why there should be any
difference in “substance” between the resemblances added
at different stages of the regress. In fact, it is hard to understand
what such a difference in “substance” would amount to in
the first place (Daly 1997 [1994]: 151–152). A more convincing
reason for thinking that the regress is benign is given instead by the
“pattern of dependence” it instantiates. For, even those
who do not think that the internality of exact resemblance makes it a
mere “pseudo-addition” to its subvenient base, agree that
resemblance, whatever it is, is such that its existence is necessarily
incurred simply given the existence of its relata. But then, no matter
how many resemblances we regressively generate, ultimately they will
all depend for their existence on the existence of the resembling
tropes, which will resemble each other because of their individual
nature, which is primitive. This means that the existence of the
regress in no way contradicts—it does not function as a
reductio against—the resemblance of the original
tropes. On the contrary, it is because the tropes resemble
each other, that the regress exists. Therefore, the regress is benign
(see e.g., Campbell 1990: 37; Maurin 2002: 78ff).

This response will only work if the nature of individual
tropes—their being what they are—is primitive and
not further analyzable (i.e., it will only work if we assume the
standard view of the nature of tropes). To see this, suppose instead
that the nature of the trope is understood in terms of the trope's
resemblance to other tropes (suppose, that is, that a resemblance
nominalism of the kind defended for ordinary concrete particulars in
Rodriguez-Pereyra 2002 is accepted). Given a resemblance nominalism of
this kind, the pattern of dependence instantiated by the resemblance
regress will be quite different from the pattern it instantiates if
the nature of the tropes is taken as primitive. For now the tropes
will resemble each other, not because of their primitive nature, but
because of the (1st order) resemblance-trope which holds
between them. And this (1st order) resemblance-trope will,
in turn, have its nature determined by the existence of the
(2nd order) resemblance-relations in which it stands to
other (resemblance-)tropes, and so on, ad infinitum. On this
view, therefore, the existence of the regress would
contradict—and hence function as a reductio
against—the resemblance of the original tropes. Perhaps for that
reason, resemblance nominalism has no explicit proponents among the
trope theorists.

A radical option, finally, is to simply opt out of the
“resemblance game.” For, if resemblance is out of the
picture then, clearly, so is the resemblance regress. One such
alternative is provided by Ehring (2011: 175ff). According to Ehring,
the trope is not what it is either primitively or because of whatever
resemblance relations it stands in to other tropes. Rather, it is what
it is, because of the natural classes to which it belongs. Distinct
objects “share” a property, moreover, if the tropes which
partly constitute them are members of the same natural class.
Why do the tropes belong to the same natural class? They belong
because they belong. It is primitive. But now, critics complain, the
order of explanation is implausibly turned on its head. Tropes do not
get sorted into natural classes in virtue of their nature, instead
they have the nature they do because they belong to this or that
natural class. Many find that this is a high price to pay for avoiding
the resemblance regress, and the view has few proponents.

The second constructive task facing the trope theorist is that of
building something that “behaves” like a concrete
particular does, using only tropes. Exactly how a concrete particular
behaves is of course a matter that can be debated. This is not a
debate to which the trope theorist has had very much, or at least not
anything very original, to contribute. Instead, the trope theoretical
discussion has been focused on an issue that arguably needs solving
before questions concerning what the concrete particular can
or cannot do become relevant. The trope theoretical discussion, more
precisely, has been focused on the issue of if and
how concrete particulars can be made up from tropes in the
first place.

According to the “standard” view, endorsed by the majority
of the trope theorists, concrete particulars are (structured or
unstructured) bundles of tropes. More precisely, a concrete particular
consists of a sufficient number of mutually
compresent tropes. What is a sufficient number? The admittedly
not very informative answer that has been given to this question is
that a sufficient number is the number of tropes it takes to turn the
many abstract tropes into one concrete whole (it is
the number of tropes required to make every need for completion
satisfied within the whole, in order to, in Husserl's
colorful terms, turn it into a “pregnant whole” ready to
give birth to an independent substance (Husserl 2001 [1900/1913])).

What is compresence? When the same question was asked about exact
resemblance, the trope theorist had the option of treating the
relation either as a real or as a “pseudo” addition to the
resembling tropes (see section 3.1). The reason
why exact resemblance could be treated as a mere “pseudo”
addition, moreover, was that it is an internal relation and
so exists necessarily simply given the existence of its relata.

Suppose that compresence is likewise internal. Then the tropes it
relates could not not be compresent. In fact,
they—provided that they all exist—could not not
be compresent with each
other.[16]
However, that the tropes that now make up
a certain concrete particular could exist and not make up that
concrete particular seems to be genuinely possible. Therefore, it has
been argued, compresence must be regarded as an external
relation and, as such, a “real” addition to the tropes it
relates.

Just as in the case of resemblance, however, if compresence is a real
addition to the tropes it relates, there will be an infinite
regress. This regress is often referred to as the “Bradley
regress” (after the regress set out in Bradley 1930 [1893]) and
it—as well as its possible solutions—has received a lot of
attention in the literature (for an overview see Maurin 2012; see also
Armstrong 1978; Vallicella 2002 and 2005; Schnieder 2004; and Cameron
2008). One interesting thing about this regress is that it seems to be
a problem not just for the trope theorist who holds that concrete
particulars are bundles of tropes, but also for the trope theorist who
thinks that the concrete particular is a substrate in which a
(sufficient) number of tropes are instantiated (a view proposed in
Martin 1980; Heil 2003; and Lowe 2006). And it seems to be a
problem for those who think that concrete particulars are bundles of
universals and for those who believe that they are substrates
in which a (sufficient) number of universals are instantiated. In
fact, according to Bradley, this is a problem for any view
according to which there can be any kind of unity in
complexity.

This regress is arguably vicious. The “pattern of
dependence” it instantiates is the opposite of that instantiated
by the resemblance regress. In the resemblance case, in order for
tropes t1, t2, and
t3 to exactly resemble each other, what is required
is that they exist. Given their (primitively natured)
existence, and given that exact resemblance is treated as a
real ontological addition (which it arguably doesn't have to be),
an infinity of resemblance-tropes can be generated. In the compresence
case, on the other hand, tropes t1,
t2, and t3 are compresent only
given that a relation-trope c1 is added to
the bundle. And c1 only turns what are many tropes
into one concrete particular given the addition of a
(2nd order) relation-trope c2 holding
between it and the rest of the tropes in the bundle. But then
c2 needs something to tie it to
c1. Enter c3. And so on. The
existence of this regress arguably contradicts—and hence
functions as a reductio against—the compresence of the
original tropes in the bundle and, thereby, the (possible) existence of
the concrete particular.

Since concrete particulars (possibly) exist, something must be wrong
with this argument. But what? One option is to question the
externality of compresence, and hold that it is internal after all.
This view has been defended primarily by those who think of tropes as
a kind of property (see Molnar 2003; Heil 2003 and 2012; see also
Armstrong 2006). For, if tropes are ways things are, they are
“non-transferable”. But if tropes are
“non-transferable”, it is argued, compresence is an
internal relation. And, if compresence is internal, then the pattern
of dependence instantiated by the regress to which it gives rise is
benign. Problem solved. Against this view it may however be objected
that if you think of tropes as ways things are, this at most
gives you a reason to think that tropes must belong to some
object. However, in order to solve the regress problem, tropes must be
“non-transferable” in the much stronger sense that they
must belong to a specific object. And, critics claim, the
only reason for accepting that tropes are
“non-transferable” in this strong sense, is that it solves
the regress problem. But this means that this is a
“solution” which cannot be independently justified (for an
account of the different senses of “non-transferable”, see
Cameron 2006; see also Maurin 2010).

Or we could do as Peter Simons has suggested (in Simons 1994; see also
Keinänen 2011; and Keinänen and Hakkarinen 2013), and view
the concrete particular as constituted, partly by a
“nucleus” made up from mutually and individually (i.e.,
internally) dependent tropes, and partly (at least in the normal case)
by a “halo” made up from tropes which depend for their
existence on the existence of the (individual tropes in the) nucleus,
although the (tropes in the) nucleus at most depends for its existence
on the existence of tropes of the same kind as the ones now
in its halo. This view arguably gives the proponent of the bundle
theory all the benefits of a substrate-attribute view, without the
embarrassment of having to accept the existence of mysterious
substrates. Even better, no regress is generated. The tropes in the
nucleus, first, are internally unified, and so nothing needs to be
added in order to bring them together. And the tropes in the halo
depend specifically on the (individual tropes in the) nucleus, which
means that their existence is enough to guarantee the existence of the
whole to which they belong. The problem with this view is that, once
again, the possibility that the tropes in the halo could exist and not
be joined to this particular nucleus is ruled out with no
(independent) justification.

According to a number of between themselves very different sorts of
trope theorists, therefore, we should stop bothering with the (nature
and dependence of the) related tropes, and investigate instead the
(special) nature of compresence itself. This seems intuitive enough.
After all, is it not the business of a relation to relate? According
to one suggestion along these lines (defended in Maurin 2010 and 2011;
and Wieland and Betti 2008; see also Robb 2005 and Mertz 1996 for
similar views), non-relational tropes have an existence that is
independent of the existence of some specific—either
non-relational or relational—trope, but relational tropes
(including compresence) depend specifically for their existence on the
very tropes they relate. This means that, if c1
exists, it must relate the tropes
t1, t2,
t3 it in fact relates, even though, from the
existence of tropes t1, t2, and
t3, it doesn't follow that they are
compresent. There is, then, no regress and except for
c1, the tropes involved in constituting the
concrete particular could exist without being compresent with each
other. That the compresence trope is an exception could be seen as
acceptable since compresence played no role when our modal intuitions
about (the constituents of) concrete particulars were
first
formed.[17]

According to Mertz (see also Maurin 2011), on this view of
compresence the Bradley regress turns into an argument for the
existence of tropes (over, or in addition to, other kinds of
entities). To be able to do the unifying work for which it is
introduced, compresence cannot be a universal. For, if it
were, then if one of the concrete particulars whose constituents it
joins cease to exist, so will every other concrete particular unified
by the same (universal) relation of compresence. But, as Mertz points
out, “this is absurdly counterfactual!” (Mertz 1996:
190). Nor could it be a state of affairs. For, states of affairs are
in themselves complexes, and so could not be used to solve the Bradley
problem. If anything, they are part of the problem, not the
solution.[18]

If you accept the existence of at least some tropes, it has been
repeatedly argued, you have the means available to solve or to
dissolve a number of serious problems, not just in metaphysics but in
philosophy generally. In what follows, the most common
trope-applications proposed in the literature are very briefly
introduced.

According to a majority of the trope theorists, tropes have an
important role to play in causation. It is, after
all, not the whole stove that burns you, it is its
temperature that does the damage. And it is not any
temperature, nor temperature in general, which leaves a red mark. That
mark is left by the particular temperature had by this particular
stove now or, in other words, it is left by the stove's
temperature-trope. Claims like these are quite common in the
trope literature (see e.g., Williams 1997 [1953]; and Campbell 1990),
although, to find those claims further elaborated is more rare (for
exceptions, see Denkel 1996; Molnar 2003; and Heil 2003).

That tropes can play a role in causation can hardly be
doubted. But can this role also provide the trope-proponent with a
reason to think that tropes exist? No, critics have argued. The role
tropes (can) play in causation does not provide the trope proponent
with any special reason to prefer an ontology of tropes over
alternative ontologies. More precisely, it does not give her any
special reason to prefer an ontology of tropes over one of states of
affairs. Just like tropes, the state of affairs is particular. Just
like tropes, it is localized. And, just like tropes, it is
non-repeatable (although it contains a repeatable item—the
universal—as one of its constituents). Every reason for thinking
that tropes are the world's basic causal relata is therefore also a
reason to think that this role is played by states of affairs.

According to Ehring, this is not true. To see why not, he asks us to
consider the following simple scenario: a property-instance at
t1 is causally responsible for an instance of
the same property at t2. This is a case of
(singularist) causation which is also a case of property
persistence. But what does property persistence involve? According
to Ehring, property persistence is not just a matter of something not
changing its properties. For, even in cases where nothing discernibly
changes, the property instantiated at t1 could
nevertheless have been replaced by another property of the same type
during the period between t1 and
t2. In order to be able to ontologically explain
the scenario set out above, therefore, we first need an account of
property persistence able to distinguish “true” property
persistence from cases of “non-salient property change” or
what may also be called property type persistence. But, Ehring
claims, this is something a theory according to which property
instances are states of affairs cannot do (this is demonstrated with
the help of a number of thought experiments, which space does not allow
me to reproduce here, but see Ehring 1997: 91ff). Therefore,
causation, and especially property persistence, gives us a special
reason to think that tropes exist (for more reasons to prefer tropes as
causal relata, see Garcia-Encinas 2009).

Not surprisingly, those who think that tropes play the role of causal
relata and of causal mechanisms in causation generally also believe
that they play that role in mental physical causal transactions
specifically. But you do not have to think that tropes are the world's
basic causal relata in order to believe that they have a role to play
in this context. To see this, suppose Lisa burns herself on the hot
stove. One of the causal transactions that then follow can be
described thus: Lisa removed her hand from the stove
because she felt pain. This is a description which seems to
pick out ‘being in pain’ as one causally relevant
property of the cause. That ‘being in pain’ is a
causally relevant property accords well with our intuitions. However,
to say it is leads to trouble. The reason for this is that mental
properties, like that of ‘being in pain’, can be realized
by physically very different systems. Therefore, mental properties
cannot be identified with physical ones. On the other hand, we
seem to live in a physically closed and causally non-overdetermined
universe. But this means that, contrary to what we have supposed so
far, Lisa did not remover her hand because she felt pain. In
general, it means that mental properties are not causally relevant,
however much they seem to be.

But if properties are tropes, some trope theorists have proposed, this
conclusion can be resisted (see Robb 1997; Martin and Heil 1999; and
Heil and Robb 2003; for a hybrid version see Nanay 2009; see also
Gozzano and Orilia 2008). To see this, we need first to disambiguate
our notion of a “property”. This notion, it is argued, is
really two notions, namely:

Property1 = that which imparts on an individual thing its
particular nature (property as token), and

Property2 = that which makes distinct things the same
(property as type).

Once “property” is disambiguated, we can see how mental
properties can be causally relevant after all. For then, if mental
properties1 are tropes, they can be identified with
physical properties1. Mental properties2 can
still be distinguished from physical properties2, for
properties considered as types are, in line with the standard
view of tropes, identified with similarity classes of tropes
(see section 3.1). When Lisa removes her hand
from the stove because she feels pain, therefore, she removes her
hand in virtue of something that is partly characterized by a
trope which is such that it belongs to a class of mentally similar
tropes. This trope is identical with a physical trope—it
is both mental and physical—because it also
belongs to a (distinct) similarity class of physically similar
tropes. Therefore, mental properties can be causally relevant in spite
of the fact that the mental is multiply realizable by the physical,
and in spite of the fact that we live in a physically closed and
non-overdetermined universe.

This suggestion has been criticized. According to Noordhof (1998: 223)
it fails because it does not respect the “bulge in the carpet
constraint.” And it does not respect that constraint because
now, the question which was ambiguously asked about properties, can be
unambiguously asked about tropes: is it in virtue of being mental or
in virtue of being physical that the trope is causally relevant for the
effect (for a response, see Robb 2001; and Ehring 2003)? And Gibb
(2004) has complained that the trope's simple and primitive nature
makes it unsuitable for membership in two such distinct and
radically different classes as that of the mentally and of the
physically similar tropes, respectively (for more reasons against the
trope-theoretical suggestion see MacDonald and MacDonald 2006).

Another important reason for thinking that tropes exist, it has been
proposed, is the role tropes play in perception. That what we perceive
are the qualities of the things rather than the things themselves,
first, seems plausible (for various claims to this effect, see
Williams 1997 [1953]: 123; and Campbell 1997 [1981]: 130). And that
the qualities we perceive are tropes rather than universals or
instantiations of universals (states of affairs) is, according to
Lowe, a matter that can be determined with reference to our
experience. Lowe argues (1998: 205) (see also, Lowe 2008; Mulligan
1999):

[W]hen I see the leaf change in colour—perhaps as it turned
brown by a flame—I seem to see something cease to exist in the
location of the leaf, namely its greenness. But it could not be the
universal greenness which ceases to exist. My opponent must say that
really what I see is not something ceasing to exist, but merely the
leaf's ceasing to instantiate greenness, or greenness ceasing to be
‘wholly present’ just here. I can only say that the
suggestion strikes me as being quite false to the phenomenology of
perception. The objects of perception seem, one and all, to be
particulars—and, indeed, a causal theory of perception (which I
myself favour) would appear to require this, since particulars alone
seem capable of entering into causal relations.

A similar view is put forth by Mulligan et al. They argue (1984:
300):

…whoever wishes to reject moments [i.e., tropes] must of course
give an account of those cases where we seem to see and hear them,
cases we report using definite descriptions such as ‘the smile
that just appeared on Rupert's face’. This means that he must
claim that in such circumstances we see not just independent things
per se, but also things as falling under certain concepts or as
exemplifying certain universals. On some accounts (Bergmann, Grossman)
it is even claimed that we see the universal in the thing. But the
friend of moments finds this counterintuitive. When we see Rupert's
smile, we see something just as spatiotemporal as Rupert himself, and
not something as absurd as a spatio-temporal entity that somehow
contains a concept or a universal.

But, a critic may object, these are not very strong reasons for thinking
that it is tropes and not states of affairs that we perceive. For the
view that our perception of a trope is not only distinct, but also
phenomenologically distinguishable, from our perception of a state of
affairs seems grounded in little more than its proponent's
introspective intuitions. Especially if tropes are waysthings are (a view held by both Lowe and Mulligan et al.),
these intuitions seem to be very fragile (see also Rodriguez-Pereyra
2002: 93–94). For more ways in which tropes have been taken to make a
difference to (our theory of) perception, see Nanay 2012 and
Almäng 2013.

That language furnishes the trope theorist with solid reasons for
thinking that there are tropes has been indicated by a number of trope
theorists and it has also been forcefully argued, especially by
Friederike Moltmann in a number of papers (see also Mertz 1996:
3–6). Taking Mulligan et al. 1984 as her point of departure,
Moltmann argues that natural language contains a number of phenomena
whose semantic treatment is best spelled out in terms of an ontology
that includes tropes.

Nominalizations, first, may seem to point in the opposite
direction. For, in the classical discussion of properties, the
nominalization of predicates such as is wise into nouns fit
to refer, has been taken to count in favor of universal realism. A
sub-class of nominalizations—such as John's
wisdom—can, however, be taken to speak in favor of the
existence of tropes. This is the sort of nominalizations which, as
Moltmann puts it, “introduce ‘new’ objects, but only
partially characterize them” (2007: 363). That these sorts of
nominalizations refer to tropes rather than to states of affairs, she
argues, can be seen once we consider the vast range of adjectival
modifiers they allow for, modifiers only tropes and not states of
affairs can be the recipients of (see especially Moltmann 2009:
62–63; see also Moltmann 2003).

Bare demonstratives, next, especially as they occur in
so-called identificational sentences, provide another reason for
thinking that tropes exist (Moltmann 2013). In combination with the
preposition like—as in Turquoise looks like
that—they straightforwardly refer to tropes. But even in
cases where they arguably do not refer to tropes, tropes nevertheless
contribute to the semantics of sentences in which they figure. In
particular, tropes contribute to the meaning of so-called
identificational sentences like ‘This is Mary’ or
‘That is a beautiful woman’. These are no ordinary
identity statements. What makes them stand out is the exceptional
neutrality of the demonstratives in subject position. According to
Moltmann, these sentences are best understood in such a way that the
bare demonstratives that figure in them do not refer to individuals
(like Mary), but rather to perceptual features (tropes) in the
situation at hand (a view that depends on taking tropes as the objects
of perception, see section
4.3). Identificational sentences, she claims, involve precisely
the identification of a bearer of a trope via the denotation (if not
reference) of a (perceptual) trope.

Comparatives—like John is happier than
Mary—finally, are according to the received view, such that
they refer to abstract objects that form a total ordering (so-called
degrees). According to Moltmann, a better way to understand these
sorts of sentences is with reference to tropes. John is happier
than Mary should hence be understood as John's happiness
exceeds Mary's happiness. This view is according to Moltmann
preferable to the standard view, because tropes are easier to live
with than “abstract, rarely explicit entities such as degrees or
sets of degrees” (Moltmann 2009: 64).

Discussions of what use can be made of tropes in science can be found
scattered in the literature. Examples include Harré's 2009
discussion of the role tropes play (and don't play) in chemistry and
Nanay's 2010 attempt to use tropes to improve on Ernst Mayr's
“population thinking” in biology. Most discussions have
however been focused on the relationship between tropes and physics
(see e.g., Kuhlmann et al. 2002). Most influential in this respect is
Campbell's field-theory of tropes (defended in his 1990: chapter 6;
see also Von Wachter 2000) and Simons' “nuclear” theory of
tropes and the scientific use he tentatively makes of it (Simons 1994;
see also Morganti 2009; and Wayne 2008).

According to Campbell, the world is constituted by a rather limited
number of field tropes which, according to our (current) best science,
ought to be identified with the fields of gravitation,
electromagnetism, and the weak and strong nuclear forces (plus a
space-time field). Standardly, these forces are understood as exerted
by bodies that are not themselves fields. Not so on Campbell's
view. Instead, matter is thought of as spread out and as present in
various strengths across a region without any sharp boundaries to its
location. What parts of the mass field we choose to focus on will be
to a certain degree arbitrary. A zone in which several fields all
sharply increase their intensity will likely be taken as one single
entity or particle but given the overall framework, individuals of
this kind are to be viewed as “well-founded appearances”
(Campbell 1990: 151).

Campbell's views have been criticized, among others by Schneider
(2006). According to Schneider, the field ontology proposed by
Campbell (and by Von Wachter) fails, because the notion of a field
with which they seem to be working, is not mathematically
rigorous.[19]
Morganti who, just like Campbell, wants to identify the tropes with
actual entities described by quantum physics, finds several problems
with the identifications actually made by Campbell, and proposes
instead that we follow Simons and identify the basic constituents of
reality with the fundamental particles, where the basic particles are
understood as bundles of tropes (Morganti 2009). By taking the basic
properties described by the Standard Model as fundamental tropes, is
the suggestion, the constitution of particles out of more elementary
constituents can be readily reconstructed (possibly by using the
formal sheaf-theoretical framework proposed by Mormann 1995, or the
algebraic framework suggested by Fuhrmann 1991).

Relatively little has so far been written on the topic of tropes in
relation to issues in moral philosophy and value theory. Two things
have however been argued. First, that tropes (and not, as is more
commonly supposed, objects or persons or states of affairs) are the
bearers of final value. Second, that moral non-naturalists (who hold
that moral facts are fundamentally autonomous from natural, or
scientific, facts) must regard properties as tropes in order to be
able to account for the supervenience of the moral on the
natural. That tropes are the bearers of (final) value has been argued
by a number or trope theorists. To say that what we value are the
particular properties of things, they have pointed out, is prima facie
intuitive (see Williams 1997 [1953]: 123). Also, whereas concrete
particulars can be the simultaneous subjects of conflicting
evaluations, this is not true of tropes, which would seem to make
tropes especially suited for the job as value-bearers
(Campbell 1997 [1981]: 130-131). Although seemingly attractive, the
view that tropes are the bearers of (final) value has received
surprisingly little attention in the (non-trope theoretical)
value-theoretical community. Two exceptions to this rule are
Rabinowicz and Rønnow-Rasmussen 2003 and Olson 2003. According
to Rabinowicz and Rønnow-Rasmussen, first, though tropes can be
the bearers of final value, they cannot be the only such
bearers, mainly because different pro-attitudes are fitting with
respect to different kinds of valuable objects. But, Olson responds,
this conclusion follows only if we assume that, to what we direct our
evaluative attitude is indicative of where value is localized. But
final value, Olson argues, should be understood strictly as the value
which something has for its own sake, which means that if e.g., a
person is valuable because of her courage, then she is not valuable
for her own sake but is valuable, rather, for the sake of one of her
properties (i.e., her tropes), which means that although the
evaluative attitude may well be directed at a person or a thing, the
person or thing is nevertheless valued because of, or for the sake of,
the tropes which characterize it.

Non-naturalists, next, are often charged with not being able to
explain what appears to be a necessary dependence of moral facts on
natural facts. Normally, this dependence is explained in terms of
supervenience, but in order for such an account to be compatible with
the basic tenets of moral non-naturalism, it has been argued, this
supervenience must, in turn, be explainable in purely non-naturalistic
terms (for an overview of this debate, see Ridge 2010). According to
Shafer-Landau (2003) (as interpreted by Ridge (2007)) this problem is
solved if moral and physical properties in the sense of kinds, are
distinguished from moral and physical properties in the sense of
tokens, or tropes. For then we can say, in analogy with what has been
suggested in the mental-physical case (see
section 4.2), that although (necessarily) every moral trope is
constituted by some concatenation of natural tropes, it does not
follow from this that every moral type is identical to a natural
type. This suggestion is criticized in Ridge 2007.

–––, 2006, “Particulars Have their Properties of
Necessity,” in Universals, Concepts and Qualities:
New Essays on the Meaning of Predicates, P. F. Strawson and A.
Chakrabarti (eds.), Aldershot: Ashgate.

Husserl, E., 2001 [1900/1913], Logical Investigations,
D. Moran (ed.), J. N. Findlay (trans.), London & New York:
Routledge. First published, in two volumes in German, in 1900 and
1901; second edition in 1913; English translation in 1970.